Related papers: Double solids, categories and non-rationality
It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted…
We use our extension of the Noether-Lefschetz theorem to describe generators of the class groups at the local rings of singularities of very general hypersurfaces containing a fixed base locus. We give several applications, including (1)…
In this note we construct an example of a smooth projective threefold that is irrational over $\mathbb Q$ but is rational at all places. Our example is a complete intersection of two quadrics in $\mathbb P^5$, and we show it has the desired…
We study the connectedness of the real locus of smooth geometrically rational Fano threefolds and prove a sufficient criterion of $\mathbb{R}$-rationality.
It is well known that a smooth projective Fano variety is rationally connected. Recently Zhang (and later Hacon and McKernan as a special case of their work on the Shokurov RC-conjecture) proved that the same conclusion holds for a klt pair…
We find a characterization for Fano 4-folds $X$ with Lefschetz defect $\delta_{X}=3$: besides the product of two del Pezzo surfaces, they correspond to varieties admitting a conic bundle structure $f\colon X\to Y$ with…
In this paper, we investigate the concepts of generalized twice differentiability and quadratic bundles of nonsmooth functions that have been very recently proposed by Rockafellar in the framework of second-order variational analysis. These…
We study a class of 3-manifolds called strong L-spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that…
Let $X$ be a smooth Fano variety and $\mathcal{K}u(X)$ the Kuznetsov component. Torelli theorems for $\mathcal{K}u(X)$ says that it is uniquely determined by a polarized abelian variety attached to it. An infinitesimal Torelli theorem for…
We present three large families of new examples of plumbed 3-manifolds that bound rational homology 4-balls. These are constructed using two operations, also defined here, that preserve the lack of a lattice embedding obstruction to…
We study when the Picard group of smooth surfaces of degree $d\geq 5$ in $\mathbb{P}^3$ acquires extra classes. In particular we show that the so called exceptional components of the Noether-Lefschetz locus are not Zariski dense. This…
This thesis contributes with a number of topics to the subject of string compactifications. In the first half of the work, I discuss the Hodge plot of Calabi-Yau threefolds realised as hypersurfaces in toric varieties. The intricate…
We prove Manin's conjecture on the asymptotic behavior of the number of rational points of bounded anticanonical height for a spherical threefold with canonical singularities and two infinite families of spherical threefolds with log…
Mirror symmetry for higher genus curves is usually formulated and studied in terms of Landau-Ginzburg models; however the critical locus of the superpotential is arguably of greater intrinsic relevance to mirror symmetry than the whole…
For each odd integer r greater than one and not divisible by three we give explicit examples of infinite families of simply and tangentially homotopy equivalent but pairwise non-homeomorphic closed homogeneous spaces with fundamental group…
We study links between algebraic cycles on threefolds and finite-dimensionality of their motives with coefficients in Q. We decompose the motive of a non-singular projective threefold X with representable algebraic part of CH_0(X) into…
We study a supersymmetric partition function of topological vortices in 3d N=4,3 gauge theories on R^2 x S^1, and use it to explore Seiberg-like dualities with Fayet-Iliopoulos deformations. We provide a detailed support of these dualities…
Let $X$ be a normal projective threefold with mild singularities, and $L_X$ a strictly nef $\mathbb{Q}$-divisor on $X$. First, we show the ampleness of $K_X+tL_X$ with sufficiently large $t$ if either the Kodaira dimension $\kappa(X)\neq 0$…
We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.
We consider Blanchet, Habegger, Masbaum and Vogel's universal construction of topological theories in dimension two, using it to produce interesting theories that do not satisfy the usual two-dimensional TQFT axioms. Kronecker's…